This matchup basically boils down to who can make the most out of their reads. Understanding what works and what doesn't work in here is even more important because the potential damage you can be taking is incredibly high, along with the fact that she can punish herself quite well and quite often with her drives.
For the most part, stay defensive and analyze what the other Noel is trying to do. If she's very aggressive, then use the appropriate normals to punish with, and the appropriate drives to invuln through obvious patterns, such as 5Ding through CR strings, or 2Ding over her lows/6Bs/throw attempts. If the Noel also plays out the reaction game, test what sort of read she is trying to get, and possibly beat it out with your own or baiting out an attempted invuln read. If they understand how to manuever during CR strings to avoid being punished, then just wait it out until she finishes her strings, and make sure to know how to block them.
There are some auto-pilot CR strings to look out for since some players will continue the string as if it comboed, instead of hit-confirming the starter, such as 5D/2D > d.6A > d.6C. You can 5D through the d.6A, and 2D over the d.6C. Just watch out for possible anti-punish strategies like being Spring Raided or Assault Throughed.
Also, some other punishes I like to do are CH 5B/5C > 3C if you block their 3C depending on the distance, and using 6A against jump-ins (although still very risky).
After understanding the other Noel's gameplan, just work on maximizing your damage output to give yourself the much needed wall carry and life lead. Noel's back-to-corner game isn't very strong until she gains 50 Heat, to which she can turn the tides on you with her Counter Assault. You can also do the same, but make sure to pick your spots. If she can guess where to punish your CA, then she can very easily put you back in the corner with a devastating combo that will net her the Heat for corner Fenrir finishes and Heat for CA if she needs it.